Is there a way to draw a pattern onto mesh and then extrude?
You may use use a Bsurfaces addon and then the Knife Project Tool. Go to User Preferences (Ctrl+Alt+U-->Add-ons) and enable it. 


Add an object you want to draw the extrusion pattern on, then add a Plane (or any other object you like), enter the Edit Mode and delete it (X). In the Properties Panel (N) add a new Grease Pencil layer, then go to the Tool Shelf (T)-->Grease Pencil and change a stroke placement to Surface. Now go to the Tool bookmark in a Tool Shelf. Draw some strokes on an object (hold D, then press LMB [ How to draw grease pencil on a surface (blender 2,75)? ]). When finished, click on Add Surface in Bsurface panel. Change the settings below as you like.


Now (being in Object Mode) select a mesh you created using a Grease Pencil, then your base mesh and enter the Edit Mode. Go to the Tool Shelf-->Tools-->Transform-->Add-->Knife Project. Now the only thing you should do is to retopologize your mesh a bit.